/*
 * Copyright (C) 2008 Apple Inc. All Rights Reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 *
 * THIS SOFTWARE IS PROVIDED BY APPLE INC. ``AS IS'' AND ANY
 * EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
 * PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL APPLE INC. OR
 * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
 * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
 * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
 * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
 * OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
 * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 */

#ifndef SKY_ENGINE_PLATFORM_ANIMATION_UNITBEZIER_H_
#define SKY_ENGINE_PLATFORM_ANIMATION_UNITBEZIER_H_

#include <math.h>
#include "flutter/sky/engine/platform/PlatformExport.h"
#include "flutter/sky/engine/wtf/Assertions.h"

namespace blink {

struct UnitBezier {
  UnitBezier(double p1x, double p1y, double p2x, double p2y) {
    // Calculate the polynomial coefficients, implicit first and last control
    // points are (0,0) and (1,1).
    cx = 3.0 * p1x;
    bx = 3.0 * (p2x - p1x) - cx;
    ax = 1.0 - cx - bx;

    cy = 3.0 * p1y;
    by = 3.0 * (p2y - p1y) - cy;
    ay = 1.0 - cy - by;

    // End-point gradients are used to calculate timing function results
    // outside the range [0, 1].
    //
    // There are three possibilities for the gradient at each end:
    // (1) the closest control point is not horizontally coincident with regard
    // to
    //     (0, 0) or (1, 1). In this case the line between the end point and
    //     the control point is tangent to the bezier at the end point.
    // (2) the closest control point is coincident with the end point. In
    //     this case the line between the end point and the far control
    //     point is tangent to the bezier at the end point.
    // (3) the closest control point is horizontally coincident with the end
    //     point, but vertically distinct. In this case the gradient at the
    //     end point is Infinite. However, this causes issues when
    //     interpolating. As a result, we break down to a simple case of
    //     0 gradient under these conditions.

    if (p1x > 0)
      m_startGradient = p1y / p1x;
    else if (!p1y && p2x > 0)
      m_startGradient = p2y / p2x;
    else
      m_startGradient = 0;

    if (p2x < 1)
      m_endGradient = (p2y - 1) / (p2x - 1);
    else if (p2x == 1 && p1x < 1)
      m_endGradient = (p1y - 1) / (p1x - 1);
    else
      m_endGradient = 0;
  }

  double sampleCurveX(double t) {
    // `ax t^3 + bx t^2 + cx t' expanded using Horner's rule.
    return ((ax * t + bx) * t + cx) * t;
  }

  double sampleCurveY(double t) { return ((ay * t + by) * t + cy) * t; }

  double sampleCurveDerivativeX(double t) {
    return (3.0 * ax * t + 2.0 * bx) * t + cx;
  }

  // Given an x value, find a parametric value it came from.
  double solveCurveX(double x, double epsilon) {
    ASSERT(x >= 0.0);
    ASSERT(x <= 1.0);

    double t0;
    double t1;
    double t2;
    double x2;
    double d2;
    int i;

    // First try a few iterations of Newton's method -- normally very fast.
    for (t2 = x, i = 0; i < 8; i++) {
      x2 = sampleCurveX(t2) - x;
      if (fabs(x2) < epsilon)
        return t2;
      d2 = sampleCurveDerivativeX(t2);
      if (fabs(d2) < 1e-6)
        break;
      t2 = t2 - x2 / d2;
    }

    // Fall back to the bisection method for reliability.
    t0 = 0.0;
    t1 = 1.0;
    t2 = x;

    while (t0 < t1) {
      x2 = sampleCurveX(t2);
      if (fabs(x2 - x) < epsilon)
        return t2;
      if (x > x2)
        t0 = t2;
      else
        t1 = t2;
      t2 = (t1 - t0) * .5 + t0;
    }

    // Failure.
    return t2;
  }

  // Evaluates y at the given x. The epsilon parameter provides a hint as to the
  // required accuracy and is not guaranteed.
  double solve(double x, double epsilon) {
    if (x < 0.0)
      return 0.0 + m_startGradient * x;
    if (x > 1.0)
      return 1.0 + m_endGradient * (x - 1.0);
    return sampleCurveY(solveCurveX(x, epsilon));
  }

 private:
  double ax;
  double bx;
  double cx;

  double ay;
  double by;
  double cy;

  double m_startGradient;
  double m_endGradient;
};

}  // namespace blink

#endif  // SKY_ENGINE_PLATFORM_ANIMATION_UNITBEZIER_H_
